Daniel Radcliffe bounds in to the hotel room like an eager puppy, all hand shakes and smiles for the assembled publicists, PAs and make-up artists. He is talking excitedly about the “gorgeous blonde” he just met in the corridor. She had asked if he could direct her to her room – not so subtly revealing her room number in the process – and he hadn’t been able to assist her. “But it wouldn’t have worked anyway,” he says, “because she was about 6ft 2in.” He’s joking, he has a girlfriend, but the point he makes about his height is an intriguing one. He is 5ft 5in. This is the first thing you notice about him, but luckily it is not the first thing the camera notices. Film cameras love a male lead whose head looks slightly too big for his body, and smaller actors are more likely to have this golden ratio than taller ones: think Alan Ladd, Humphrey Bogart, James Dean, Dustin Hoffman, Tom Cruise and so on.

Today, at 23, Radcliffe looks limber and lean in jeans and checked shirt, with prominent dark eyebrows and wide blue eyes. Almost in parody of his cameo for Ricky Gervais’s Extras – he played himself as a horny teenager desperate to look rebellious – he tells me he is “addicted to nicotine” and needs to have a cigarette before we begin our interview. He rolls one up and smokes it out of the window.

I ask if this is a privilege of film stars. “They let me do it here so that I don’t have to stand outside,” he says. “There will be photographers, not for me, but just because they hang around smart hotels like this. It’s pretty much the only thing I exploit my position for, to be allowed to smoke inside.” Well I should think a lot of the time he doesn’t have to exploit his position because “his people” exploit it for him, clearing a path, booking the best table and so on. “I try not to let that stuff happen, but yes, it could be happening without me knowing. I don’t have an entourage in my personal life. I get driven here and I get driven home, but that’s it. I hate that kind of dropping a name to get a table stuff. Maybe it’s an English thing that there’s just some sort of embarrassment saying: ‘Hello, I’m Daniel Radcliffe, does that make a difference to you?’”

That he qualifies his comment about the photographers by saying that they won’t necessarily be waiting for him is telling. His modesty, self-deprecation and good manners are instantly apparent, and a great credit to his parents who managed to forge a well-rounded and functional personality out of potentially dysfunctional circumstances.

If anything, Radcliffe seems slightly too eager not to appear starry or arrogant. He tells me he never does drugs, having seen the effects they have on people. And after a few too many drinking binges that ended in blackouts he gave up alcohol in 2010. He has said in the past that he was a “really annoying, loud, inappropriate, messy drunk”.

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Was it that when he was drunk he revealed a side of his personality he didn’t like? “It wasn’t that I became a nasty person at all, it was just that I felt that I was running away from thinking about things. It was a way of ignoring all my own fears about ‘Will I be able to keep going in this business after the Harry Potter series ends?’ You know, it was a way of, I think, coping with that. And it was a very bad way of coping with that.”

Well, there was life for him in the film world after Potter. On the morning I meet him the papers are all carrying stories about the film he starred in earlier this year: The Woman in Black, which has become the highest-grossing British horror in 20 years, taking more than $127 million around the world. The stories, which he hasn’t had a chance to see, are about how The Woman in Black has become the most complained about film of the year, because even though it was 12A, parents took their young children to it. “Oh that,” he says, looking relieved when I tell him why he is in the papers. “I do take a small tincture of pride about it being the most complained-about film. I would have thought from the trailer that you could sense what kind of a movie it was going to be. I said at the time, if your kid is under 12, I would advise them not to see this film. Apparently there was a girl at the British premier who fainted and when I heard that, I was, like, ‘we did something right’.” (A film he stars in next year may prove even more traumatic for Harry Potter fans; in Horns, he plays a man who suddenly sprouts devil horns, and who may or may not be a killer.)

That film was something of a rite of passage for Radcliffe, an emphatic signal that he had moved on from Harry Potter. “There was a part of me in some scenes that was slightly scared of my own face, because I know that my face is…” He trails off. “I’m scared of any sort of expression looking like a Harry expression, and so I think that the journey for me in the last year is kind of about acceptance, of going, ‘This is my face and it was also the face that played Harry’. I have to stop fighting that aspect, and not worry about being expressive at times. As far as I can tell, most actors’ main motivation is self-doubt and neuroses.”

I ask if he felt a great weight on his shoulders as an 11 year-old when he was chosen as the star of what was expected to be a blockbuster franchise? I mean, that first film could have failed; people could have said it isn’t as good as the book and the whole thing could have fizzled out. Was it stressful? “Not at that age. I didn’t start to feel that pressure until much later. I think probably, that’s one of the best things about Chris Columbus [the director], he made the process so enjoyable we never thought of it as anything but fun, and it really wasn’t until the third film that I started going ‘OK, now I want to really dedicate myself to this and start learning about acting and getting better’.’’

That he was working alongside some of the greats of British film and theatre – Alan Rickman, Michael Gambon, Gary Oldman – meant that he was learning from the best. Indeed there was little point in him going to Rada after he left school – not that he went to school, having had tutors on the set instead. But what about university? “I got my ASs but dropped out before taking my As because I figured university is something you do to find out what you want to do, and I knew what I wanted to do, and I was already doing it.” His co-star Emma Watson (Hermione) was able to combine the two, though. Did he not fancy doing that? “Well fair play to her, but I don’t think that I could have done that. And bear in mind, I did well in my GCSEs and my AS-levels, I got good grades and I was happy with them, but Emma’s grades made mine look pretty f------ shabby, you know. Emma is seriously academic.”

Besides, he is a voracious reader of poetry and fiction, as I discover when he tells me about Kill Your Darlings, the low budget but artistically uncompromised film he made after The Woman in Black, which is due to be released next year. He plays the poet Allen Ginsberg and his knowledge about and passion for the Beat Generation is certainly impressive; Radcliffe can talk at length about Ginsberg’s journey from middle-class conformity to the world of “rich, moneyed libertines”.

He’s also amusing about what it was like playing a gay man. “I was in a position that I had not been in before,” he recalls. “It was slightly odd, but that film was shot so rapidly there was no time for prudishness or for worry.” On the subject of his love life – he’s straight, by the way – he says it is much easier dating girls who are in the film world because “they can be relaxed about all the time you have to be on location, and the love scenes you have to do. Where you’re kissing someone else, that takes a bit of getting used to, for everybody. And even when I went out with an actress who was having to do a love scene with somebody, I was like ‘Erm… I’m not sure I’m going to watch that’. It is always a weird thing, there’s no getting away from that.

“The Ginsberg film wasn’t so much of a problem in that respect because it was mainly men that I was interested in for that.”

Before that film is released there will be another literary outing, this time a TV miniseries. A Young Doctor’s Notebook is a black comedy set during the Russian Revolution adapted from several short stories by his favourite Russian writer, Mikhail Bulgakov. His co-star is Mad Men’s Jon Hamm, who will play the same character, a doctor, in an older guise. “I think they were going to release it in the spring of next year,” says Radcliffe, who adds that he’s “immensely flattered” that he might one day turn into Hamm. “And then they were, like, ‘Let’s release it at Christmas, because there’s lots of snow in it’. It’s not remotely festive, but it’s snowing all the time.”

During filming he says he learnt quite a lot about how to amputate limbs. “And I do think I could probably perform a tracheotomy now."

In terms of his role choices, you have to admire the determination with which he has avoided anything that can be compared to Harry Potter, especially when you consider how much pressure he must have been under to consolidate on his success in that role. Before the Ginsberg and the Bulgakov he had an even more unexpected stage debut, at the age of 18 in 2007. It was in Equus, Peter Shaffer’s controversial play about sexual deviation.

“That was a signal of intent,” he says now. “Looking back, that’s probably the most important choice I’ve ever made, in terms of things outside of Potter, because it showed people that I’m not just here to capitalise on the fame that I’ve got from Potter for as long as I can. That’s not what I’m about. I’m playing a much longer game than that.”

The part entailed a nude scene that prompted the inevitable headline “Harry gets his wand out”. But it was worth it. Charles Spencer of The Daily Telegraph hailed Radcliffe’s “dramatic power” and “electrifying stage presence”. For most men, I say, exposing yourself in front of a crowd of strangers is the stuff of nightmares. So what was it like? “It’s odd the first couple of times you do it, but it does just become a job. Looking back, I do think I was probably braver then than I am now. I spoke to a friend who did Hair, and he said: ‘I like getting naked on stage, it’s fun’ and I said: ‘You were in Hair! You got naked for, like, a minute, and it’s an ensemble with loads of naked people. Mine was on my own and lasted 10 minutes!’ ”

His life so far is hard to empathise with, I say – he’s the richest person under 30 in this country, for example – but I wonder whether his teens were all that different from everyone else’s. When I was that age, as I recall, I was rather self-conscious. Was self-consciousness ever an option for him, given that he was by then used to having his face projected on cinema screens and billboards across the land?

“You can still be self-conscious in my position. And shy. Shyness displays itself differently in me. I think it’s more an awkwardness. Like when I go to those events, like the Baftas, or like I was invited to this thing called the Met Ball, and I ended up having a good night because I took a friend, but normally I feel very awkward at events like that.”

Because? “Because I don’t feel that I’m good at small talk, and I’m not… You know, meeting people in that fleeting way, I never know how to give an accurate impression of myself, so I just become nervous, and stumbley.”

When people recognise him in the street, do they say “Hey, there’s Harry Potter!” or do they say “There’s Daniel Radcliffe”? “I’d be lying if I said I didn’t get Harry Potter at all. Of course I do. But you know what? I’d say the split is now rather encouragingly in favour of Daniel Radcliffe, which is rather lovely. I walked past two girls on a bench the other day, and I heard them both go ‘Oh my God, it’s Daniel Radcliffe’, and every time that happens I think: ‘Yesss!’ Not because they recognise me, because they use my name.”

One’s teenage years are awkward enough without having to live them in a spotlight, I say. Did he have people around him helping him deal with the pressures of fame – therapists, I suppose I mean? “You know, the people I talk to are my mum and dad. They are amazing people, and were always great at making me aware of which parts of it were real and which weren’t, and making me aware of which parts were important and which were not.”

It helped that they were in the business, he says. His father, Alan, is a former literary agent, who gave up his job to chaperone his son when he was chosen from thousands to play Harry Potter. His mother, Marcia, is a casting agent, who put him forward for that fateful audition.

So even though he was growing up on film sets, where the whole world was apparently revolving around him, his parents managed to keep his ego in check? “I don’t think that’s in me to be honest. I’ve not got… I’ve always had, like, from the age of about 11, I’ve had such an intolerance for bad behaviour of actors that I don’t think I was ever going to be that person.” What about the financial side of things? “I have an amazing lawyer, and I have my mum, and I have my accountant, who was my mum’s accountant when she was young. He’s called Keith and he’s also brilliant.”

I imagine Keith knows how much young Daniel is worth, but does Daniel know? “I do not, no. I hear things said, but I don’t know if any of them are true. And I never want to seem ungrateful for it all, but the money is not a motivating factor in my life. Also,” he adds with a laugh, “I would be the last person who should be left in charge of it, frankly. Because I am so terrible at maths. Not that I’d blow it or anything, but I just wouldn’t do anything with it.”

Thanks to his mother’s investment skills, then, he owns several properties in London and New York, as well as an impressive art collection including works by Damien Hirst and Craigie Aitchison. His personal fortune has been estimated as being not unadjacent to £50 million. Should the estimate be higher or lower? “I’m not going to play this guessing game,” he says politely but firmly. “I’m just not.”

His politeness seems to be one of his defining characteristics. For his own part he has, in the past, described himself as nerdy, hyperactive and skittish, and you can see little hints of those things in his personality, too. But no one seems to have a bad word to say about him, and that, all things considered, is quite an achievement.

It is time for his photograph and so we return to the other room. A change of shirt is needed and Radcliffe strips off to reveal an impressive six-pack, and biceps that can only have come from hours in the gym. And, yes, he does this completely without self-consciousness.

‘Playhouse Presents…A Young Doctor’s Notebook’ begins on December 6 at 9pm on Sky Arts 1. See sky.com/arts